Nonparametric estimation of a convex bathtub-shaped hazard function. (English) Zbl 1200.62025

Summary: We study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of \(n^{2/5}\) at points \(x_{0}\) where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of the nonparametric MLE studied here is that no arbitrary choice of the tuning parameter (or complicated data-adaptive selection of the tuning parameter) is required.


62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62N02 Estimation in survival analysis and censored data
62E20 Asymptotic distribution theory in statistics


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